One known technology for measuring fluid velocity is ultrasound. Ultrasound velocity meters may be attached externally to pipes, or ultrasound transducers may be placed internal to pipes. Fluid flow may be measured by multiplying fluid velocity by the interior area of a pipe. Cumulative fluid volume may be measured by integrating fluid flow over time.
FIG. 1 illustrates an example of positioning ultrasonic transducers for fluid velocity measurement. There are many alternative configurations, and FIG. 1 is just an example for the purpose of illustrating some basic equations for ultrasound measurement of fluid velocity. In FIG. 1, two ultrasonic transducers UT1 and UT2 are mounted inside a pipe 100 and a fluid is flowing in the pipe 100. Let L be the distance between the ultrasonic transducers UT1 and UT2. Let θ be the angle between a line connecting the transducers and the wall of the pipe. Let t12 be the propagation time (also known as time-of-flight) for an ultrasonic signal from ultrasonic transducer UT1 to ultrasonic transducer UT2, and let t21 be the propagation time for an ultrasonic signal from ultrasonic transducer UT2 to ultrasonic transducer UT1. Let c be the velocity of ultrasound in the fluid, and let v be the velocity of fluid flow. The propagation times are as follows.
            t      12        =          L              c        +                  v          ⁡                      [                          cos              ⁡                              (                θ                )                                      ]                                          t      21        =          L              c        -                  v          ⁡                      [                          cos              ⁡                              (                θ                )                                      ]                              
Typically, the angle θ and the distance L are known and the objective is measure the velocity v of the fluid. If the velocity c of ultrasound in the fluid is known, then only one propagation time (t12 or t21) is needed. However, the velocity c of ultrasound in the fluid is a function of temperature, and a temperature sensor may or may not be included depending on the target cost of the system. In addition, a flow meter may be used for multiple different fluids (for example, water or gas). Measuring two different propagation times (t12 and t21) enables elimination of the variable c. Combining the above equations and eliminating the variable c yields the following equation for fluid velocity v.
  v  =            L      2        *                            t          21                -                  t          12                                      t          21                ⁢                  t          12                    
Therefore, to determine fluid velocity without knowing the velocity of ultrasound in the fluid, measurements of two ultrasonic propagation times (t12 and t21) are needed. There is an ongoing need for improved measurement of ultrasonic propagation times.